I have a dataset X which consists of two parts: X1 and X2. X2 is believed to depend on X1. And there is a resulting dataset Y which depends on both X1 and X2. For every training sample X1 and X2 are vectors of integers from limited range - roughly speaking, 50 numbers in X1 and about 1000 in X2. Y is a single integer also within some range.
The problem is predicting Y based on both X1 and X2 in a training set and only X1 in a test set.
I'm going to use neural networks, but I doubt what type of NN should I choose to be able to predict Y having only partial data X1, while training on both X1 and X2. That's because training only on X1 doesn't give a good accuracy, so I decided to engage additional data X2, which, I believe, could tell more about features from X1. However, data from X2 are not available when predicting new samples.
My idea is elaborate new features using X2, which are associated with particular values from X1, and hence will be useful for predicting new samples. Say, I assign kind of score to each particular value from X1. My assumption is that score will remain valid for all new samples with unknown X2, but well known values from X1 which have assigned "scores". In this case we get an additional features, which can be useful.
Does such a problem have a common name and what methods would you suggest to solve it?
See comments below for details of my particular case.
Originally posted at StackOverflow.